document.write( "Question 386103: Find the vertices, foci, and minor axis: (x-1)^2/21 + (y-3)^2/4 = 1 \n" ); document.write( "
Algebra.Com's Answer #273019 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28x-1%29%5E2%2F21+%2B+%28y-3%29%5E2%2F4+=+1\"\r\n" );
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document.write( "That is the form: \r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1\"\r\n" );
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document.write( "because a is always greater than b in an ellipse.\r\n" );
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document.write( "It has center (h,k) = (1,3), semi-major axis = a = \"sqrt%2821%29\",\r\n" );
document.write( "and semi-minor axis = b = \"sqrt%284%29=2\"\r\n" );
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document.write( "It has its major axis horizontal because aČ is under the term in x\r\n" );
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document.write( "We plot the center:\r\n" );
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document.write( "We draw the complete major axis \"a+=+sqrt%2821%29\", about 4.6 units right and\r\n" );
document.write( "left from the center (in green).  The endpoints of the major axes are the\r\n" );
document.write( "vertices. Since the vertices are \"sqrt%2821%29\" units right and left of the\r\n" );
document.write( "center, their coordinates are (1 ± \"sqrt%2821%29\",3)\r\n" );
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document.write( "We draw the complete minor axis \"b+=+2\" units above and below\r\n" );
document.write( "the center (also in green):\r\n" );
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document.write( "We sketch in the ellipse:\r\n" );
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document.write( "Finally we find the foci which are c units from the center and are\r\n" );
document.write( "located on the major axis, where \r\n" );
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document.write( "\"c+=+sqrt%28a%5E2-b%5E2%29=sqrt%2821-4%29=sqrt%2817%29\", about 4.1 units.\r\n" );
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document.write( "So the coordinates of the foci are (1 ± \"sqrt%2817%29\",3)\r\n" );
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document.write( "I'll plot them.  They are just inside the ellipse on each end:\r\n" );
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document.write( "Edwin
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